Guaranteed safe online learning of a bounded system

For some time now machine learning methods have been widely used in perception for autonomous robots. While there have been many results describing the performance of machine learning techniques with regards to their accuracy or convergence rates, relatively little work has been done on developing theoretical performance guarantees about their stability and robustness. As a result, many machine learning techniques are still limited to being used in situations where safety and robustness are not critical for success. One way to overcome this difficulty is by using reachability analysis, which can be used to compute regions of the state space, known as reachable sets, from which the system can be guaranteed to remain safe over some time horizon regardless of the disturbances. In this paper we show how reachability analysis can be combined with machine learning in a scenario in which an aerial robot is attempting to learn the dynamics of a ground vehicle using a camera with a limited field of view. The resulting simulation data shows that by combining these two paradigms, one can create robotic systems that feature the best qualities of each, namely high performance and guaranteed safety.